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The impact of numeracy on reactions to different graphic risk presentation formats: An experimental analogue study

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Wright, Alison J., Whitwell, Sophia C. L., Takeichi, Chika, Hankins, Matthew and Marteau, Theresa M. (2009) The impact of numeracy on reactions to different graphic risk presentation formats: An experimental analogue study. British Journal of Health Psychology, 14 (1). pp. 107-125. ISSN 1359107X

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The impact of numeracy on reactions todifferent graphic risk presentation formats:An experimental analogue study

Alison J. Wright1*, Sophia C. L. Whitwell1, Chika Takeichi1,Matthew Hankins1,2 and Theresa M. Marteau1

1Health Psychology Section, Department of Psychology, King’s College London,London, UK

2Brighton and Sussex Medical School, Brighton, East Sussex, UK

Objectives. Numeracy, the ability to process basic mathematical concepts, may affectresponses to graphical displays of health risk information. Displays of probabilistic riskinformation using grouped dots are easier to understand than displays using disperseddots. However, dispersed dots may better convey the randomness with which healththreats occur, so increasing perceived susceptibility. We hypothesized that low numeracyparticipants would better understand risks presented using grouped dot displays, whilehigh numeracy participants would have good understanding, regardless of display type.Moreover, we predicted that dispersed dot displays, in contrast to grouped dot displays,would increase risk perceptions and worry only for highly numerate individuals.

Design and method. One hundred and forty smokers read vignettes asking themto imagine being at risk of Crohn’s disease, in a 2(display type: dispersed/groupeddots) £ 3(risk magnitude: 3%/6%/50%) £ 2(numeracy: high/low) design. They com-pleted measures of risk comprehension, perceived susceptibility and worry.

Results. More numerate participants had better objective risk comprehension, butthis effect was not moderated by display type. There was marginally significant supportfor the predicted numeracy £ display type interaction for worry about Crohn’sdisease, but not for perceived susceptibility to the condition.

Conclusions. Dispersed dot displays somewhat increase worry in highly numerateindividuals, but only numeracy influenced objective risk comprehension. The mosteffective display type for communicating risk information will depend on the numeracyof the population and the goal(s) of the communication.

Communicating probabilistic risk information is a key challenge for health

professionals. Effective risk communication strategies are needed, so that individuals

can make informed choices about their treatments and their health-related behaviours.

* Correspondence should be addressed to Dr Alison J. Wright, Health Psychology Section, Department of Psychology, King’sCollege London, London SE1 9RT, UK (e-mail: [email protected]).

TheBritishPsychologicalSociety

107

British Journal of Health Psychology (2009), 14, 107–125

q 2009 The British Psychological Society

www.bpsjournals.co.uk

DOI:10.1348/135910708X304432


The introduction of large population screening programmes in the UK and elsewhere,

such as that for bowel cancer (NHS bowel cancer screening programme, 2007) and

cardiovascular disease risk assessments ( Joint British Societies, 2005) means that many

more individuals will receive probabilistic risk information. Moreover, new

technologies, such as genetic testing for predisposition to common diseases, create

further demand for effective risk communication strategies.This study was conducted to inform the design of participant information in a trial

assessing the impact of genetic risk information on behaviour change (ISRCTN

21633644). Participants in the trial undergo risk assessments for Crohn’s disease.

Crohn’s disease runs in families, individuals with an affected first degree relative having

an elevated probability of developing the condition (Lewis et al., 2007). Smoking also

increases the likelihood that individuals at risk develop Crohn’s disease (Selby, 2003).

Learning that one is susceptible to Crohn’s disease, but that stopping smoking reduces

this risk, may motivate smokers to quit. However, the best way to communicatethe probabilities involved has yet to be determined. In previous trials assessing the

impact of genetic risk information on behaviour change, participants had difficulties

comprehending the risk information (Lipkus, McBride, Pollak, Lyna, & Bepler, 2004).

Graphic displays are thought to facilitate probabilistic risk communication

(Ancker, Senathirajah, Kukafka, & Starren, 2006). Graphic formats may make the

perception of risk information easier for individuals, so decreasing the cognitive

processing demands of the information. Reducing the cognitive effort required to

use information in decision-making can lead to its greater use (Hibbard & Peters, 2003),and reduce judgment errors (Feldman-Stewart, Kocovski, McConnell, Brundage,

& Mackillop, 2000).

Several studies have examined which graphic formats are most effective at

communicating probabilistic risk information. Based on a recent review of these

(Ancker et al., 2006), it was decided to use icon arrays to communicate risk

information. Icon arrays portray a risk using a group of individual icons such as dots,

oblongs, or human figures. Such arrays have several desirable properties for risk

communication. Firstly, individuals understand probabilities better when they arepresented at the discrete level, rather than as proportions or percentages (Berry,

2004). Secondly, icon arrays allow individuals to view two or more probabilities

expressed in terms of a common denominator. Comparing ‘4 in 1,000’ to ‘1 in 1,000’

is easier than comparing ‘1 in 250’ to ‘1 in 1,000’ (Cosmides & Tooby, 1996;

Gigerenzer & Hoffrage, 1995).

Icon displays can make part to whole relationships clearly visible. When icons are

arranged as a group, the ability to estimate what proportion object A fills of the larger

object B appears to be automatic (Stone et al., 2003). Alternatively, icons can bearranged so that those ‘affected’ appear randomly scattered throughout the array. Such

dispersed icon displays may help convey the randomness inherent in health risks, so

increasing perceived vulnerability to the health outcome, although there is an absence

of evidence to support or refute this (Baty et al., 1997; Schapira, Nattinger, & McHorney,

2001). However, dispersed icon displays make it difficult for viewers to estimate the

proportion affected as this can only be estimated by counting, rather than by judging the

proportion of the block area.

Several studies have compared the effects of different types of icon display.Participants who viewed grouped displays were more accurate at judging the larger of

two risks, at estimating the magnitude of the difference between two probabilities and

at judging the magnitude of a single probability (Feldman-Stewart et al., 2000). In a study

108 Alison J. Wright et al.


examining the ability of grouped displays, dispersed displays and bar graphs to convey

breast cancer risk information, participants perceived the magnitude of a 9% risk to

be higher when it was presented using a dispersed icon display than when it was

presented as either a grouped icon display or as a bar graph (Schapira, Nattinger, &

McAuliffe, 2006).

Evidence that individuals may prefer grouped displays to dispersed displays comesfrom a focus group study (Schapira et al., 2001), in which participants disliked dispersed

displays because the only way to understand the magnitude of the probability was to

count the affected icons. Therefore, while dispersed icon displays may increase

perceived susceptibility to a condition and so potentially promote risk-reducing

behaviour (Milne, Sheeran, & Orbell, 2000), participants’difficulties understanding such

displays could result in the risk information not being comprehended, and so failing to

motivate risk-reducing behaviour.

Numeracy and the communication of health risk informationOne individual difference likely to affect reactions to graphic displays of probabilistic

risk information is numeracy, ‘the ability to process basic probability and numerical

concepts’ (Peters et al., 2006b). There is considerable individual variation in numeracy.

Even within a highly educated sample, up to 20% of participants had difficultyanswering simple questions, such as choosing the option that represented the highest

risk from three different proportions or percentages (Lipkus, Samsa, & Rimer, 2001).

Numeracy may affect reactions to risk information for several reasons. People with high

numeracy are more fluent in converting percentages to frequencies and vice versa. They

may also experience more affect in response to numbers conveying probabilistic risk

information, and may use this affect more in guiding their decisions (Peters et al.,

2006b). Affect can influence decision-making by serving as information (Clore, Gasper,

& Garvin, 2001), individuals basing their decisions on how the alternatives make themfeel. Alternatively, the extent and valence of affect can alter how the information is

processed and thus influence decisions (Nabi, 1999; O’Keefe, 2002; Peters, Lipkus, &

Diefenbach, 2006a).

Evidence suggests that numeracy may moderate reactions to probabilistic risk

information and to graphic displays of such information. In a study of women’s ability

to apply information regarding the benefits of mammography to their estimated

lifetime risk of breast cancer, women with high numeracy were more accurate in

applying the risk reduction information, whereas less numerate participantsoverestimated the benefits of mammography to their lifetime cancer risk (Schwartz,

Woloshin, Black, & Welch, 1997). Another study found that participants perceived

risks of breast cancer as greater when presented with dispersed, compared to

grouped, displays, but that this effect was more pronounced for individuals with low

numeracy (Schapira et al., 2006).

In presenting risk information to motivate behaviour change, the communication has

two goals: to enable individuals to understand the size of the risk estimates provided;

and to alter participants’ perceived susceptibility to the condition in order to motivaterisk-reducing behaviour change. Compared to grouped displays, dispersed displays may

increase individuals’ appreciation of the role of chance in whether adverse health

outcomes occur and this may increase perceived susceptibility to these outcomes.

However, because dispersed displays are harder to comprehend, this effect may be

limited to numerate individuals.

Numeracy and risk communication 109


The present studyThe present study uses vignettes to investigate smokers’ reactions to risk information

about the likelihood of developing Crohn’s disease, and how these reactions differ

according to icon display type and participants’ numeracy. The likelihood of developing

Crohn’s disease conditional on continued smoking was varied systematically, to examine

the effects of display type at different levels of risk magnitude. We examine participants’subjective and objective understanding of the risk estimates contained in the vignette,

their perceived likelihood of, and their worry about, developing Crohn’s disease.

Individual’s appraisals of susceptibility to a health event are likely to be related to their

levels of worry as worry can be regarded as an affective perception of likelihood (Klein

& Stefanek, 2007). However, perceived likelihood and worry are only moderately

correlated (Lipkus et al., 2000), and both may make separate contributions to predicting

motivation for health behaviours. As numerate individuals may be more subject to

extracting affect from probabilistic risk information, they may experience more worryabout their risk of Crohn’s disease for a given risk magnitude than less numerate

individuals. This may be moderated by display type. Dispersed displays, which highlight

the role of chance in whether one develops Crohn’s disease, may produce more affect.

However, this effect may be restricted to more numerate participants, as it requires the

ability to extract meaning from the more complex, dispersed display.

Hypotheses

(1) Understanding of risk estimates† Grouped displays are easier to process than dispersed displays, leading to better

understanding of risk estimates, an effect that will be stronger for people with

low numeracy.

(2) Perceived susceptibility to Crohn’s disease† Higher magnitude risk estimates will lead to greater perceived susceptibility to

Crohn’s disease.† Dispersed displays will result in participants reporting greater perceived

susceptibility to Crohn’s disease than grouped displays, but this effect will be

weaker for people with low numeracy.(3) Worry about developing Crohn’s disease

† Higher magnitude risk estimates lead to greater worry about developing Crohn’s

disease.† Dispersed displays will result in participants reporting greater worry about

developing Crohn’s disease than grouped displays, but this effect will be weaker

for people with low numeracy.

Methods

DesignParticipants were randomly allocated to read one of six vignettes, asking them to

imagine being given information about their risk of Crohn’s disease, in a 2(display type:dispersed or grouped) £ 3(risk magnitude: 3, 6, or 50%) design. This study is part of a

broader study that also examined the effects of risk provenance (genetic test vs. family

history only). The results of the risk provenance manipulations are presented in a

separate paper (Wright, Takeichi, Whitwell, Hankins, & Marteau, 2008).



VignettesTo reflect potential clinical applications of genetic testing for Crohn’s disease, each

vignette asked participants to imagine that they had a sibling with Crohn’s disease,

and provided information about the condition’s symptoms. Participants imagined

undergoing a risk assessment, to ascertain their own risk of developing Crohn’s

disease. They were then presented with their hypothetical risk assessment results.To understand the probabilities involved, participants imagined 1,000 smokers with

the same result, who also had sibling with Crohn’s disease. Depending on the

magnitude condition, participants were told 30 (3% risk), 60 (6% risk), or 500 (50%

risk) of the 1,000 people were expected to develop Crohn’s disease. This was

illustrated in a 40 £ 25 array of dots. In the grouped display conditions, a triangular

section, starting at the bottom right-hand corner of the array, of the same number

of dots as people expected to develop Crohn’s disease, was coloured in. In the

dispersed display conditions, the same number of dots was coloured as in thegrouped display conditions, but the coloured dots were dispersed throughout

the entire display. In all conditions, participants were informed that stopping

smoking could halve their risk, and this was illustrated. Finally, participants learnt

that in the general population about one in 1,000 people are expected to develop

Crohn’s disease. The full vignettes are shown in the Appendix.

MeasuresObjective risk comprehension was assessed by asking participants: ‘Which of the three

sets of risk figures you were given was the biggest risk and which was the smallest risk?’

with the options ‘my chances of developing Crohn’s disease’, ‘my chances of developing

Crohn’s disease if I stopped smoking’, and ‘the general population chance of Crohn’s

disease’. In all conditions, the correct responses were that the general population

chance of Crohn’s disease was the smallest and the chance of developing Crohn’s

disease was the biggest.Subjective ease of understanding was assessed using a single item, ‘How easy did

you find it to understand the information we gave you about the chances of developing

Crohn’s disease?’ rated 1: ‘very difficult’ – 7: ‘very easy’.

Perceived susceptibility to Crohn’s disease was assessed using three items, reflecting

different aspects of perceived susceptibility (Weinstein, 1998). Susceptibility condi-

tional on continued smoking was assessed using ‘If you continue to smoke, how likely

do you think it is that you will develop Crohn’s disease?’ rated 1: ‘not at all’ – 7: ‘extremely

likely’. Susceptibility conditional on quitting smoking was assessed using ‘If you stopsmoking, how likely do you think it is that you will develop Crohn’s disease?’ rated 1:

‘not at all’ – 7: ‘extremely likely’. Susceptibility relative to other smokers was assessed

using ‘Compared to other smokers the same age as you, what do you think your chance

of developing Crohn’s disease is?’ rated: 1: ‘a lot more’, 2: ‘more’, 3: ‘average’, 4: ‘less’, 5:

‘a lot less’.

Worry about developing Crohn’s disease was assessed using 3 items (a ¼ :96)

(Cameron & Diefenbach, 2001): ‘To what extent are you worried about getting Crohn’s

disease?’, ‘To what extent are you concerned about getting Crohn’s disease?’, and ‘Towhat extent are you afraid of getting Crohn’s disease’, all rated 1: ‘not at all’ – 7:

‘extremely’.

Numeracy was assessed using eight items developed by Lipkus and his

colleagues (2001).



Demographic information and smoking behaviourParticipants were asked their age, gender, and educational qualifications. Nicotine

dependence was assessed using the Heaviness of Smoking Index (HSI; Heatherton,

Kozlowski, Frecker, Rickert, & Robinson, 1989).

ParticipantsThe Research Ethics Committee of a UK university approved the study. One hundred

and forty adult smokers, who did not have Crohn’s disease, were recruited from a

market research agency’s nationally representative internet panel. Panel members

complete surveys in return for ‘points’ that are exchangeable for consumer goods.Participants received 10 ‘points’ (approximate monetary value £1). This sample size is

sufficient to detect medium-sized (0.5 SD) main effects and interactions with a type I

error rate of 0.05 and a type II error rate of 0.8.

Sixty-one (43.6%) men and 79 (56.4%) women participated. Their mean (SD) age was

44.3 (13.5) years. Twelve (8.6%) had no formal educational qualifications, 30 (27.9%)

had qualifications usually completed at age 16 (GCSEs/O Levels), 34 (24.3%) had

qualifications usually completed at age 18 (A Levels or further education qualifications)

and 46 (32.9%) had a University degree. Nine participants had other qualifications. Theirmean (SD) HSI score was 2.6 (1.6), indicating a moderate level of nicotine dependence.

ProcedurePanel members were e-mailed a URL that linked to the survey. Participants first

completed the demographic and smoking behaviour items. Next, they read one of the

six vignettes, randomly allocated by the website software. Participants then completed

the main questionnaire, which began by assessing risk perceptions, then worry,perceived ease of understanding, objective understanding, and finished with the

numeracy items. While responding to the questionnaire, participants could choose to

view the risk information again, in a separate window.

Analyses overviewThe effects of display type and numeracy on subjective ease of understanding were

assessed using ANOVA. The effects of display type and numeracy on objective risk

comprehension were assessed using logistic regression ( Jaccard, 2001). The interaction

term’s ability to significantly contribute to the prediction of risk comprehension was

tested using a hierarchical regression strategy. For the perceived risk measures andworry, the effects of display type, risk magnitude, numeracy and their interactions were

examined using ANOVA. Significant interactions were probed using simple main effects

analysis, employing a Sidak adjustment for multiple comparisons. As dichotomizing

scales to create a two level factor may yield misleading results (MacCallum, Zhang,

Preacher, & Rucker, 2002), we did not dichotomize the numeracy scale using a median

split on the total scores. Instead, we subjected the items to psychometric analysis, and

then used the best discriminating item as a marker of numeracy.

Results

Numeracy levels in this sampleTable 1 shows the proportions of participants answering each numeracy item

correctly. The median score was seven, as it was in Lipkus et al.’s (2001) sample.



However, the participants performed differently on the items, being less likely to

correctly answer items 1–4, but more likely to correctly answer items 5–7 andsomewhat more likely to answer item eight correctly. Psychometric analysis1 of the scale

revealed that the first item had the highest variance (SD ¼ 0:49) and a good item-total

correlation (r ¼ :62). This item also had the second highest difficulty score (0.59)

(where difficulty is defined as the mean item score and thus, for a dichotomous item, the

proportion of participants getting it right), the highest discrimination value (0.83) (Allen

& Yen, 1979), indicating that it was the best item for discriminating between the top

third and bottom third of total scores on the numeracy measure, and a very good value

for Ferguson’s delta for discrimination (0.97) (Hankins, 2007). Therefore, participantswho answered this item correctly were treated as having higher numeracy, while those

who did not were considered to have lower numeracy.

Table 1. Proportion of correct responses to the numeracy scale made by the 140 participants,

in relation to the findings of Lipkus et al. (2001)

Item

Percentage (N)answering correctly

(N ¼ 140)

Percentage of participantsanswering correctly in

Lipkus et al.’s (2001) study

Which of the following numbersrepresents the biggest risk of gettinga disease: 1 in 100 risk of getting adisease/1 in 1,000 risk of getting adisease/1 in 10 risk of getting a disease

58.6 (82) 78.2

Which of the following numbers representsthe biggest risk of getting a disease:1% risk of getting a disease/10% riskof getting a disease/5% risk of getting a disease

76.4 (107) 83.6

If person A’s risk of getting a disease is1% in 10 years, and person B’s riskis double that of A’s, what is B’s risk?

85.7 (120) 90.5

If person A’s chance of getting a disease is1 in 100 in 10 years, and person B’srisk is double that of A’s, what is B’s risk?

77.1 (108) 86.6

If the chance of getting a disease is 10%,how many people would be expectedto get the disease out of 100?

88.6 (124) 80.8

If the chance of getting a disease is 10%,how many people would be expectedto get the disease out of 1,000?

87.9 (123) 77.5

If the chance of getting a disease is 20 outof 100, this would be the same ashaving a __% chance of getting the disease

76.4 (107) 70.4

The chance of getting a viral infection is .0005.Out of 10,000 people, about how manyof them are expected to get infected?

50.7 (71) 48.6

1 Full details of the psychometric analysis of the numeracy scale are available from the first author upon request.



The high and low numeracy groups did not differ in terms of mean age, nicotine

dependence, the proportions of men and women they contained or in terms of

highest educational qualification. This latter finding echoes Lipkus et al.’s (2001)

observation that even individuals with university-level education may not be highly

numerate.

Effects of display type and numeracy on subjective ease of understandingMean subjective ease of understanding scores were high across all groups, ranging from

5.3 (SD ¼ 1:8) in the dispersed display, low numeracy condition to 5.7 (SD ¼ 1:4) in the

grouped display, high numeracy condition. Neither display type (Fð1; 136Þ ¼ 0:05,

p ¼ :82, partialh2 , :001), numeracy (Fð1; 136Þ ¼ 1:15, p ¼ :29, partialh2 ¼ :008) northeir interaction (Fð1; 136Þ ¼ 0:35, p ¼ :55, partialh2 ¼ :003) significantly influenced

subjective ease of understanding.

Effects of display type and numeracy on objective risk comprehensionTable 2 shows the results of the logistic regression predicting risk comprehension.

The percentages of participants responding correctly are shown in Table 3 and

illustrated in Figure 1. Adding the display type £ numeracy interaction term tothe model predicting correct comprehension did not improve its fit at a

statistically significant level, x2ð1Þ ¼ 1:55, p ¼ :21. Display type did not significantly

influence the odds of participants having correct objective risk comprehension.

The coefficient for numeracy in Table 2 means that the odds of having good objective

understanding for high numeracy individuals are nearly four times the odds of

having good comprehension for low numeracy individuals. This effect is conditioned

on the moderator variable (display) being equal to zero, and so applies only to

participants who viewed a grouped display. If the display variable is recoded, withzero corresponding to the dispersed display condition, then the odds ratio for

numeracy is 10.2. This indicates that when individuals saw a dispersed display,

the odds of participants with high numeracy responding correctly were 10 times the

odds of participants with low numeracy responding correctly. The coefficient for

the interaction term reflects the ratio of these two odds ratios. That the interaction

coefficient is not significant indicates that this ratio of ratios does not differ

significantly from one. In summary, while numeracy influences objective risk

comprehension, display type does not moderate its impact.

Table 2. Logistic regression predicting objective risk comprehension

95% C.I. for odds ratio

Odds ratio Lower Upper p

Display type 0.442 0.152 1.284 .134Numeracy 3.830 1.301 11.280 .015Display type £ numeracy 2.663 0.567 12.517 .215Constant 1.077 .847

Note. Dummy variable coding was as follows: Display type: grouped ¼ 0, dispersed ¼ 1; Numeracy:low numeracy ¼ 0, high numeracy ¼ 1.



The effects of display type, risk magnitude and numeracy on risk perceptionsand worryTable 4 shows mean scores by experimental group for perceived susceptibility and

worry. Table 5 details the ANOVA results for these variables.

For perceived risk conditional on continued smoking, the predicted main effect of

risk magnitude was not significant. Instead, a significant risk magnitude £ numeracyinteraction was observed. When numeracy was low, risk magnitude did not

affect risk perceptions (simple main effect (SME) of magnitude at low numeracy,

Fð2; 128Þ ¼ 1:267, p ¼ :285, partialh2 ¼ :019). However, when numeracy was

higher, risk magnitude influenced perceived risk more strongly, although the SME

was only marginally significant (Fð2; 128Þ ¼ 2:369, p ¼ :098, partialh2 ¼ :036).

Sidak-adjusted pairwise comparisons showed that, among individuals with high

numeracy, those in the 50% risk condition perceived greater susceptibility than those

in the 3% risk condition.For risk relative to other smokers, there was a marginally significant main effect of

numeracy: participants with high numeracy perceived themselves as more at risk of

Table 3. Proportions of participants correctly responding to the risk comprehension item, by

numeracy and display type

Response

Numeracy Display type Correct Incorrect

Lower Dispersed N 10 21% 32.3 67.7

Grouped N 14 13% 51.9 48.1

Higher Dispersed N 34 7% 82.9 17.1

Grouped N 33 8% 80.5 19.5

Figure 1. Proportions of participants providing a correct response to the objective risk

comprehension item, according to numeracy and display type.



Crohn’s disease relative to other smokers (mean ¼ 2:53, where low scores indicate

greater perceived risk) than did participants with low numeracy (mean ¼ 2:80).

There was also a significant risk magnitude £ display type interaction. SMEs analysis

showed that display type did not significantly influence relative risk perceptions forparticipants in the 3% group (mean relative risk ¼ 2:77 for dispersed display, 2.47 for

grouped display, SME of display Fð1; 128Þ ¼ 1:09, p ¼ :30, partialh2 ¼ :008) or those in

the 50% group (mean relative risk ¼ 2:76 for dispersed display, 2.75 for grouped display,

Fð1; 128Þ , 0:001, p ¼ :984, partialh2 , :001). However, participants who received a

6% risk estimate, and saw a dispersed display had significantly stronger relative risk

perceptions (mean ¼ 2:17, where low scores indicate greater perceived risk) than those

viewed the same risk magnitude illustrated by a grouped display (mean ¼ 3:07, SME of

display Fð1; 128Þ ¼ 11:03, p ¼ :001, partialh2 ¼ :079).Perceived susceptibility conditional on quitting was not significantly predicted by

any of the factors in the model, or their interactions.

For worry about developing Crohn’s disease, the interaction between display type

and numeracy attained marginal statistical significance and is illustrated in Figure 2.

Inspection of means suggested that, in line with predictions, dispersed displays caused

more worry for highly numerate participants than for less numerate participants, while the

difference between more and less numerate participants viewing a grouped display was

smaller, and in the other direction. However, neither of the SMEs was statistically significant(SME of numeracy for dispersed displays: Fð1; 128Þ ¼ 2:47, p ¼ :118, partialh2 ¼ :019;

SME of numeracy for grouped displays: Fð1; 128Þ ¼ 0:814, p ¼ :369, partialh2 ¼ :006).

Discussion

This study examined the effects of numeracy and display type on reactions to risk

information about Crohn’s disease. The first hypothesis was that grouped displays would be

Table 4. Perceived susceptibility and worry (mean (SD)), according to display type, risk magnitude,

and numeracy level

Variable Numeracy Display 3% 6% 50%

Risk conditional on continued Lower Dispersed 4.00 (1.70) 3.75 (1.76) 3.89 (1.27)smoking (1–7) Grouped 5.00 (1.26) 4.11(1.76) 3.67 (0.89)

Higher Dispersed 3.64 (1.15) 4.42(1.16) 4.53 (1.36)Grouped 3.67 (1.33) 3.69 (1.44) 4.40 (1.35)

Risk conditional on quitting Lower Dispersed 2.80 (1.23) 2.67 (1.23) 2.33 (1.00)smoking (1–7) Grouped 3.33 (0.82) 2.56 (1.13) 2.58 (1.62)

Higher Dispersed 2.71 (0.91) 2.75 (0.75) 2.87 (1.30)Grouped 2.56 (1.20) 2.54 (0.88) 2.60 (1.07)

Risk relative to other smokers Lower Dispersed 2.90 (1.10) 2.42 (0.79) 3.11 (0.33)(rated 1: a lot more Grouped 2.17 (0.98) 3.22 (1.20) 3.00 (0.74)– 5: a lot less) Higher Dispersed 2.64 (0.50) 1.92 (0.79) 2.40 (1.06)

Grouped 2.78 (1.17) 2.92 (0.86) 2.50 (0.97)Worry (1–7) Lower Dispersed 2.93 (2.14) 3.22 (1.52) 3.59 (2.32)

Grouped 4.06 (2.34) 3.67 (1.31) 3.75 (1.22)Higher Dispersed 3.57 (1.79) 3.75 (1.63) 4.40 (1.69)

Grouped 3.31 (1.77) 3.74 (1.60) 3.20 (1.79)



easier to understand than dispersed displays, an effect that would be particularly

pronounced for individuals with low numeracy. The results for subjective understanding

did not support this hypothesis. Responses to the subjective understanding measure

may be affected by social desirability bias, participants being unwilling to admit

to comprehension difficulties. Also, the item asked about understanding of the risk

information in general terms, rather than specifically about understanding of the

probabilities. Even participants who had difficulty understanding the numerical riskestimates may have felt that, overall, they understood the vignette well, and responded

accordingly. Future studies should frame subjective ease of understanding questions to

be more specific regarding the part(s) of the risk information about which participants

should rate their subjective comprehension.

The results for objective risk comprehension also failed to support the hypothesis.

Less numerate participants were less likely to correctly answer the objective risk

comprehension item, but this effect was not modified by display type. Neither display

type enabled less numerate participants to understand the risk information as well as didmore numerate participants. The ability of other display types to facilitate probabilistic

Table 5. Results of risk magnitude £ display type £ numeracy ANOVAs on risk perceptions

and worry

Variable Effect df a F p Partial h2

Risk conditional on Magnitude 2 0.102 .903 .002continued smoking Display type 1 0.044 .834 , .001

Numeracy 1 0.002 .964 , .001Magnitude £ display type 2 0.877 .418 .014Magnitude £ numeracy 2 3.331 .039 .049Display type £ numeracy 1 1.842 .177 .014Magnitude £ display type £ numeracy 2 0.608 .546 .009

Risk conditional Magnitude 2 0.625 .537 .010on quitting Display type 1 0.001 .977 , .001

Numeracy 1 0.043 .837 , .001Magnitude £ display type 2 0.251 .778 .004Magnitude £ numeracy 2 1.049 .353 .016Display type £ numeracy 1 1.194 .277 .009Magnitude £ display type £ numeracy 2 0.194 .824 .003

Risk relative to Magnitude 2 0.304 .738 .005other smokers Display type 1 1.554 .215 .012

Numeracy 1 2.948 .088 .023Magnitude £ display type 2 5.132 .007 .074Magnitude £ numeracy 2 2.059 .132 .031Display type £ numeracy 1 1.761 .187 .014Magnitude £ display type £ numeracy 2 0.457 .634 .007

Worry about Magnitude 2 0.248 .781 .004Crohn’s disease Display type 1 0.020 .887 , .001

Numeracy 1 0.170 .681 .001Magnitude £ display type 2 0.886 .415 .014Magnitude £ numeracy 2 0.109 .897 .002Display type £ numeracy 1 3.002 .086 .023Magnitude £ display type £ numeracy 2 0.254 .776 .004

a df error ¼ 128 for all analyses.



risk comprehension in individuals with low numeracy requires investigating. The

discrepancy in the effect of numeracy between subjective and objective risk

comprehension echoes previous findings that participants’ subjective levels of

confidence in their ability to use medical statistics were only weakly correlated withtheir objective understanding (Woloshin, Schwartz, & Welch, 2005).

For perceptions of susceptibility to Crohn’s disease, two effects were predicted.

The first was an interaction between display type and numeracy, dispersed displays

resulting in greater perceived susceptibility than grouped displays, but this effect being

weaker for less numerate participants. However, this interaction was not significant

for any of the perceived susceptibility variables. It appears that when grouped

and dispersed icon displays are presented alongside written descriptions of the

probabilities, neither type of display influences risk perceptions. There was limitedevidence that numeracy alone influenced perceived susceptibility. More numerate

participants reported greater risk relative to other smokers than did less numerate

participants. However, this difference was only marginally statistically significant.

More numerate participants may have been more able to use the probabilities presented

in the vignettes to guide their responses to the susceptibility items than were less

numerate participants. Given that all participants were told that their risks were greater

than that of the general population, perceiving higher susceptibility relative to others

seems a rational response by numerate participants to the vignette probabilities.The predicted main effect of risk magnitude on perceived susceptibility was not

significant for any of the susceptibility items. However, there was a significant

interaction between risk magnitude and numeracy on perceived susceptibility

conditional on continued smoking, the type of susceptibility perception probably

most likely to be affected by the risk information presented. More numerate participants

appeared to be influenced by the risk magnitudes presented in the vignettes, while less

numerate participants were not. Therefore, the lack of significant main effects of risk

magnitude may be due to there being considerable variance in the extent to which moreand less numerate participants’ susceptibility perceptions were influenced by the

vignette probabilities, with this variance then resulting in the main effect of risk

magnitude not being statistically significant.

There was also a significant interaction between risk magnitude and display on

susceptibility relative to other smokers, display type only making a difference to relative

Figure 2. Mean worry scores, according to numeracy and display type.



risk individuals in the 6% group. From a psychological standpoint, it is unclear as to why

display type only influenced relative risk for this particular risk magnitude. Further work

should explore the effects of display types at different levels of risk magnitude.

Finally, for worry about Crohn’s disease, two effects were predicted. The first was an

interaction between display type and numeracy, dispersed displays resulting in greater

worry than grouped displays, but this effect being weaker for less numerateparticipants. This interaction was marginally significant. As predicted, the dispersed

displays were associated with greater worry in more numerate participants than in less

numerate participants. However, contrary to prediction, grouped displays were

associated with greater worry in less numerate participants, although the absolute

magnitude of this difference between the two numeracy groups was not as pronounced

as that for dispersed displays. Given that the interaction between numeracy and display

type was only marginally significant, it requires replication. However, we might consider

these findings reason to build tentatively on Peters et al.’s (2006b) suggestion that highlynumerate individuals are more sensitive to the affective meaning of probabilistic risk

information, to also suggest that highly and less numerate individuals’ ability to extract

affective meaning from probabilistic risk information may vary according to how that

information is presented.

The predicted significant main effect of risk magnitude on worry was not observed.

Although there was a linear increase in mean worry scores across the three levels of risk

magnitude, the differences were small. Emotional responses to vignettes may be less

strong than those to real-world health risk information. Future studies should investigatewhether the effects of display type, risk magnitude and numeracy on worry are stronger

in clinical contexts.

Strengths and limitations of the current study and recommendations for furtherresearchThis is one of the first studies to examine whether numeracy moderates cognitive andemotional responses to risk estimates presented using different graphical formats. The

study benefits from using a sample with a wider range of educational backgrounds than

has hitherto been the case (Lipkus et al., 2001) and so the results may better generalize to

patient populations. While the smoking behaviour of participants in this study was very

similar to that of British smokers in general (Goddard, 2006), the internet-based

recruitment strategy may have disproportionately excluded socially deprived individuals.

Future research should attempt to examine the relationship between numeracy

and reactions to graphical displays of probabilistic risk information in such populations.Using vignettes allowed participants to be allocated to different risk magnitudes,

regardless of their smoking behaviour, so removing one potential confound in studies of

reactions to health risk information (Croyle, Sun, & Hart, 1997). However, vignettes are

obviously only representations of real-life situations, albeit representations intended to

focus attention on the experimental constructs of interest. The extent to which these

results generalize to individuals receiving probabilistic risk information in clinical

contexts remains to be seen.

There are several issues with the measures employed in this study. Items assessingworry were not conditional on continued smoking. Although worry is often assessed in

this manner (Cameron & Diefenbach, 2001), measurement error may have been

inadvertently introduced into the worry measure, some participants reporting lower

levels of worry about Crohn’s disease because they planned to quit smoking in the near



future, but others reporting worry about developing Crohn’s disease contingent on

continued smoking. We operationalised numeracy using the item that best

discriminated individuals with high and low total numeracy scores in our sample.

This introduces a small additional degree of measurement error into the analyses, which

may be partly responsible for the lack of significant effects of numeracy. However, many

of the effect sizes associated with numeracy were small, and unlikely to attain statisticalsignificance in this sample, even if numeracy was measured more precisely. A further

limitation was that, to reduce response burden, many constructs were assessed using

single items. Further studies should use multiple items to assess both risk perceptions

and risk comprehension. Finally, we operationalised perceived susceptibility in several

different ways and performed ANOVAs on each item, potentially inflating the family wise

type I error rate. Therefore, some of the significant effects observed may be due to type I

error. However, if future studies replicate these findings, we would be more confident in

our conclusions.

How should probabilistic risk information be displayed?Dispersed displays did not consistently increase perceptions of susceptibility to Crohn’sdisease. There was only marginally significant evidence that they caused greater worry

than grouped displays in more numerate participants. Therefore, any benefit of display

type for motivating behaviour change may be limited to numerate individuals. Display

type also failed to facilitate risk comprehension. Given these findings, further research is

required before we can confidently recommend a particular display type for

communicating probabilistic risk information. In particular, the triangular grouping of

icons in this study differs from the linear grouping of icons used in other studies (Feldman-

Stewart et al., 2000). Pilot work suggested that individuals preferred this triangulargrouping, but further research should compare these two types of grouped displays.

Finally, the current study focused on a situation where the goal was to increase

perceptions of susceptibility. The optimal display to employ when probabilistic risk

communications are intended either to promote informed choices between treatment

options, or to reduce over-exaggerated perceptions of susceptibility, remains an

empirical question. Health professionals wishing to communicate probabilistic risk

information to their patients need to consider the target population and the goal(s) of

the communication when deciding which graphical display to employ.

Acknowledgements

This study was conducted as part of a programme of research funded by the Medical Research

Council (‘Risk communication in preventative medicine: Optimizing the impact of DNA risk

information’, MRC ref. G0500274). The first author is funded by a Wellcome Trust Research

Training Fellowship in Health Service Research (ref. 062183/Z/00/Z).

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Appendix.

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